@misc{WinklerCherstvy2014,
  author    = {Winkler, Roland G. and Cherstvy, Andrey G.},
  title     = {Strong and weak polyelectrolyte adsorption onto oppositely charged curved surfaces},
  series = {Advances in polymer science},
  volume    = {255},
  journal   = {Advances in polymer science},
  editor    = {Muller, M.},
  publisher = {Springer},
  address   = {Berlin},
  isbn      = {978-3-642-40734-5; 978-3-642-40733-8},
  issn      = {0065-3195},
  doi       = {10.1007/12_2012_183},
  pages     = {1 -- 56},
  year      = {2014},
  abstract  = {Polyelectrolytes are macromolecules composed of charged monomers and exhibit unique properties due to the interplay of their flexibility and electrostatic interactions. In solution, they are attracted to oppositely charged surfaces and interfaces and exhibit a transition to an adsorbed state when certain conditions are met concerning the charge densities of the polymer and surface and the properties of the solution. In this review, we discuss two limiting cases for adsorption of flexible polyelectrolytes on curved surfaces: weak and strong adsorption. In the first case, adsorption is strongly influenced by the entropic degrees of freedom of a flexible polyelectrolyte. By contrast, in the strong adsorption limit, electrostatic interactions dominate, which leads to particular adsorption patterns, specifically on spherical surfaces. We discuss the corresponding theoretical approaches, applying a mean-field description for the polymer and the polymer-surface interaction. For weak adsorption, we discuss the critical adsorption behavior by exactly solvable models for planar and spherical geometries and a generic approximation scheme, which is additionally applied to cylindrical surfaces. For strong adsorption, we investigate various polyelectrolyte patterns on cylinders and spheres and evaluate their stability. The results are discussed in the light of experimental results, mostly of DNA adsorption experiments.},
  language  = {en}
}
@article{WangMetzlerCherstvy2022,
  author    = {Wang, Wei and Metzler, Ralf and Cherstvy, Andrey G.},
  title     = {Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and models},
  series = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies},
  volume    = {24},
  journal   = {Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies},
  number    = {31},
  publisher = {RSC Publ.},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/d2cp01741e},
  pages     = {18482 -- 18504},
  year      = {2022},
  abstract  = {How does a systematic time-dependence of the diffusion coefficient D(t) affect the ergodic and statistical characteristics of fractional Brownian motion (FBM)? Here, we answer this question via studying the characteristics of a set of standard statistical quantifiers relevant to single-particle-tracking (SPT) experiments. We examine, for instance, how the behavior of the ensemble- and time-averaged mean-squared displacements-denoted as the standard MSD < x(2)(Delta)> and TAMSD <<(delta(2)(Delta))over bar>> quantifiers-of FBM featuring < x(2) (Delta >> = <<(delta(2)(Delta >)over bar>> proportional to Delta(2H) (where H is the Hurst exponent and Delta is the [lag] time) changes in the presence of a power-law deterministically varying diffusivity D-proportional to(t) proportional to t(alpha-1) -germane to the process of scaled Brownian motion (SBM)-determining the strength of fractional Gaussian noise. The resulting compound "scaled-fractional" Brownian motion or FBM-SBM is found to be nonergodic, with < x(2)(Delta >> proportional to Delta(alpha+)(2H)(-1) and <(delta 2(Delta >) over bar > proportional to Delta(2H). We also detect a stalling behavior of the MSDs for very subdiffusive SBM and FBM, when alpha + 2H - 1 < 0. The distribution of particle displacements for FBM-SBM remains Gaussian, as that for the parent processes of FBM and SBM, in the entire region of scaling exponents (0 < alpha < 2 and 0 < H < 1). The FBM-SBM process is aging in a manner similar to SBM. The velocity autocorrelation function (ACF) of particle increments of FBM-SBM exhibits a dip when the parent FBM process is subdiffusive. Both for sub- and superdiffusive FBM contributions to the FBM-SBM process, the SBM exponent affects the long-time decay exponent of the ACF. Applications of the FBM-SBM-amalgamated process to the analysis of SPT data are discussed. A comparative tabulated overview of recent experimental (mainly SPT) and computational datasets amenable for interpretation in terms of FBM-, SBM-, and FBM-SBM-like models of diffusion culminates the presentation. The statistical aspects of the dynamics of a wide range of biological systems is compared in the table, from nanosized beads in living cells, to chromosomal loci, to water diffusion in the brain, and, finally, to patterns of animal movements.},
  language  = {en}
}
@article{WangCherstvyMetzleretal.2022,
  author    = {Wang, Wei and Cherstvy, Andrey G. and Metzler, Ralf and Sokolov, Igor M.},
  title     = {Restoring ergodicity of stochastically reset anomalous-diffusion processes},
  series = {Physical Review Research},
  volume    = {4},
  journal   = {Physical Review Research},
  edition   = {1},
  publisher = {American Physical Society},
  address   = {College Park, Maryland, United States},
  issn      = {2643-1564},
  doi       = {10.1103/PhysRevResearch.4.013161},
  pages     = {013161-1 -- 013161-13},
  year      = {2022},
  abstract  = {How do different reset protocols affect ergodicity of a diffusion process in single-particle-tracking experiments? We here address the problem of resetting of an arbitrary stochastic anomalous-diffusion process (ADP) from the general mathematical points of view and assess ergodicity of such reset ADPs for an arbitrary resetting protocol. The process of stochastic resetting describes the events of the instantaneous restart of a particle's motion via randomly distributed returns to a preset initial position (or a set of those). The waiting times of such resetting events obey the Poissonian, Gamma, or more generic distributions with specified conditions regarding the existence of moments. Within these general approaches, we derive general analytical results and support them by computer simulations for the behavior of the reset mean-squared displacement (MSD), the new reset increment-MSD (iMSD), and the mean reset time-averaged MSD (TAMSD). For parental nonreset ADPs with the MSD(t)∝ tμ we find a generic behavior and a switch of the short-time growth of the reset iMSD and mean reset TAMSDs from ∝ _μ for subdiffusive to ∝ _1 for superdiffusive reset ADPs. The critical condition for a reset ADP that recovers its ergodicity is found to be more general than that for the nonequilibrium stationary state, where obviously the iMSD and the mean TAMSD are equal. The consideration of the new statistical quantifier, the iMSD—as compared to the standard MSD—restores the ergodicity of an arbitrary reset ADP in all situations when the μth moment of the waiting-time distribution of resetting events is finite. Potential applications of these new resetting results are, inter alia, in the area of biophysical and soft-matter systems.},
  language  = {en}
}
@misc{WangCherstvyMetzleretal.2022,
  author    = {Wang, Wei and Cherstvy, Andrey G. and Metzler, Ralf and Sokolov, Igor M.},
  title     = {Restoring ergodicity of stochastically reset anomalous-diffusion processes},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-56037},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-560377},
  pages     = {013161-1 -- 013161-13},
  year      = {2022},
  abstract  = {How do different reset protocols affect ergodicity of a diffusion process in single-particle-tracking experiments? We here address the problem of resetting of an arbitrary stochastic anomalous-diffusion process (ADP) from the general mathematical points of view and assess ergodicity of such reset ADPs for an arbitrary resetting protocol. The process of stochastic resetting describes the events of the instantaneous restart of a particle's motion via randomly distributed returns to a preset initial position (or a set of those). The waiting times of such resetting events obey the Poissonian, Gamma, or more generic distributions with specified conditions regarding the existence of moments. Within these general approaches, we derive general analytical results and support them by computer simulations for the behavior of the reset mean-squared displacement (MSD), the new reset increment-MSD (iMSD), and the mean reset time-averaged MSD (TAMSD). For parental nonreset ADPs with the MSD(t)∝ tμ we find a generic behavior and a switch of the short-time growth of the reset iMSD and mean reset TAMSDs from ∝ _μ for subdiffusive to ∝ _1 for superdiffusive reset ADPs. The critical condition for a reset ADP that recovers its ergodicity is found to be more general than that for the nonequilibrium stationary state, where obviously the iMSD and the mean TAMSD are equal. The consideration of the new statistical quantifier, the iMSD—as compared to the standard MSD—restores the ergodicity of an arbitrary reset ADP in all situations when the μth moment of the waiting-time distribution of resetting events is finite. Potential applications of these new resetting results are, inter alia, in the area of biophysical and soft-matter systems.},
  language  = {en}
}
@article{WangCherstvyLiuetal.2020,
  author    = {Wang, Wei and Cherstvy, Andrey G. and Liu, Xianbin and Metzler, Ralf},
  title     = {Anomalous diffusion and nonergodicity for heterogeneous diffusion processes with fractional Gaussian noise},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {102},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {1},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.102.012146},
  pages     = {012146-1 -- 012146-16},
  year      = {2020},
  abstract  = {Heterogeneous diffusion processes (HDPs) feature a space-dependent diffusivity of the form D(x) = D-0|x|(alpha). Such processes yield anomalous diffusion and weak ergodicity breaking, the asymptotic disparity between ensemble and time averaged observables, such as the mean-squared displacement. Fractional Brownian motion (FBM) with its long-range correlated yet Gaussian increments gives rise to anomalous and ergodic diffusion. Here, we study a combined model of HDPs and FBM to describe the particle dynamics in complex systems with position-dependent diffusivity driven by fractional Gaussian noise. This type of motion is, inter alia, relevant for tracer-particle diffusion in biological cells or heterogeneous complex fluids. We show that the long-time scaling behavior predicted theoretically and by simulations for the ensemble-and time-averaged mean-squared displacements couple the scaling exponents alpha of HDPs and the Hurst exponent H of FBM in a characteristic way. Our analysis of the simulated data in terms of the rescaled variable y similar to |x|(1/(2/(2-alpha)))/t(H) coupling particle position x and time t yields a simple, Gaussian probability density function (PDF), PHDP-FBM(y) = e(-y2)/root pi. Its universal shape agrees well with theoretical predictions for both uni- and bimodal PDF distributions.},
  language  = {en}
}
@article{WangCherstvyKantzetal.2021,
  author    = {Wang, Wei and Cherstvy, Andrey G. and Kantz, Holger and Metzler, Ralf and Sokolov, Igor M.},
  title     = {Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {104},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Institute of Physics},
  address   = {Woodbury, NY},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.104.024105},
  pages     = {27},
  year      = {2021},
  abstract  = {How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does stochastic resetting impact nonergodicity? We examine, both analytically and by simulations, the implications of resetting on the MSD- and TAMSD-based spreading dynamics of particles executing fractional Brownian motion (FBM) with a long-time memory, heterogeneous diffusion processes (HDPs) with a power-law space-dependent diffusivity D(x) = D0|x|gamma and their "combined" process of HDP-FBM. We find, inter alia, that the resetting dynamics of originally ergodic FBM for superdiffusive Hurst exponents develops disparities in scaling and magnitudes of the MSDs and mean TAMSDs indicating weak ergodicity breaking. For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD and observe a new trimodal form of the probability density function. For reset FBM, HDPs and HDP-FBM we compute analytically and verify by simulations the short-time MSD and TAMSD asymptotes and long-time plateaus reminiscent of those for processes under confinement. We show that certain characteristics of these reset processes are functionally similar despite a different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicitybreaking parameter EB as a function of the resetting rate r. For all reset processes studied we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate r and EB similar to(1/r )-decay at large r. Alongside the emerging MSD-versus-TAMSD disparity, this r-dependence of EB can be an experimentally testable prediction. We conclude by discussing some implications to experimental systems featuring resetting dynamics.},
  language  = {en}
}
@article{WangCherstvyChechkinetal.2020,
  author    = {Wang, Wei and Cherstvy, Andrey G. and Chechkin, Aleksei V. and Thapa, Samudrajit and Seno, Flavio and Liu, Xianbin and Metzler, Ralf},
  title     = {Fractional Brownian motion with random diffusivity},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {53},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {47},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/aba467},
  pages     = {34},
  year      = {2020},
  abstract  = {Numerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments. Here, we address the case of non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise. We study the ergodic properties of this model via examining the ensemble- and time-averaged mean-squared displacements as well as the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the latter. For long measurement times, interesting crossover behaviour is found as function of the correlation time tau characterising the diffusivity dynamics. We unveil that at short lag times the EB parameter reaches a universal plateau. The corresponding residual value of EB is shown to depend only on tau and the trajectory length. The EB parameter at long lag times, however, follows the same power-law scaling as for fractional Brownian motion. We also determine a corresponding plateau at short lag times for the discrete representation of fractional Brownian motion, absent in the continuous-time formulation. These analytical predictions are in excellent agreement with results of computer simulations of the underlying stochastic processes. Our findings can help distinguishing and categorising certain nonergodic and non-Gaussian features of particle displacements, as observed in recent single-particle tracking experiments.},
  language  = {en}
}
@article{VinodCherstvyWangetal.2022,
  author    = {Vinod, Deepak and Cherstvy, Andrey G. and Wang, Wei and Metzler, Ralf and Sokolov, Igor M.},
  title     = {Nonergodicity of reset geometric Brownian motion},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {105},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {1},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.105.L012106},
  pages     = {4},
  year      = {2022},
  abstract  = {We derive. the ensemble-and time-averaged mean-squared displacements (MSD, TAMSD) for Poisson-reset geometric Brownian motion (GBM), in agreement with simulations. We find MSD and TAMSD saturation for frequent resetting, quantify the spread of TAMSDs via the ergodicity-breaking parameter and compute distributions of prices. General MSD-TAMSD nonequivalence proves reset GBM nonergodic.},
  language  = {en}
}
@article{VinodCherstvyMetzleretal.2022,
  author    = {Vinod, Deepak and Cherstvy, Andrey G. and Metzler, Ralf and Sokolov, Igor M.},
  title     = {Time-averaging and nonergodicity of reset geometric Brownian motion with drift},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {106},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {3},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.106.034137},
  pages     = {36},
  year      = {2022},
  abstract  = {How do near-bankruptcy events in the past affect the dynamics of stock-market prices in the future? Specifically, what are the long-time properties of a time-local exponential growth of stock-market prices under the influence of stochastically occurring economic crashes? Here, we derive the ensemble- and time-averaged properties of the respective "economic" or geometric Brownian motion (GBM) with a nonzero drift exposed to a Poissonian constant-rate price-restarting process of "resetting." We examine-based both on thorough analytical calculations and on findings from systematic stochastic computer simulations-the general situation of reset GBM with a nonzero [positive] drift and for all special cases emerging for varying parameters of drift, volatility, and reset rate in the model. We derive and summarize all short- and long-time dependencies for the mean-squared displacement (MSD), the variance, and the mean time-averaged MSD (TAMSD) of the process of Poisson-reset GBM under the conditions of both rare and frequent resetting. We consider three main regions of model parameters and categorize the crossovers between different functional behaviors of the statistical quantifiers of this process. The analytical relations are fully supported by the results of computer simulations. In particular, we obtain that Poisson-reset GBM is a nonergodic stochastic process, with generally MSD(Delta) not equal TAMSD(Delta) and Variance(Delta) not equal TAMSD(Delta) at short lag times Delta and for long trajectory lengths T. We investigate the behavior of the ergodicity-breaking parameter in each of the three regions of parameters and examine its dependence on the rate of reset at Delta/T << 1. Applications of these theoretical results to the analysis of prices of reset-containing options are pertinent.},
  language  = {en}
}
@article{ThapaLukatSelhuberUnkeletal.2019,
  author    = {Thapa, Samudrajit and Lukat, Nils and Selhuber-Unkel, Christine and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Transient superdiffusion of polydisperse vacuoles in highly motile amoeboid cells},
  series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
  volume    = {150},
  journal   = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
  number    = {14},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0021-9606},
  doi       = {10.1063/1.5086269},
  pages     = {18},
  year      = {2019},
  abstract  = {We perform a detailed statistical analysis of diffusive trajectories of membrane-enclosed vesicles (vacuoles) in the supercrowded cytoplasm of living Acanthamoeba castellanii cells. From the vacuole traces recorded in the center-of-area frame of moving amoebae, we examine the statistics of the time-averaged mean-squared displacements of vacuoles, their generalized diffusion coefficients and anomalous scaling exponents, the ergodicity breaking parameter, the non-Gaussian features of displacement distributions of vacuoles, the displacement autocorrelation function, as well as the distributions of speeds and positions of vacuoles inside the amoeba cells. Our findings deliver novel insights into the internal dynamics of cellular structures in these infectious pathogens. Published under license by AIP Publishing.},
  language  = {en}
}